you can target outlook.com (and Outlook Web App for that matter, which is a totally different thing and a very dark place) by adding the attribute selecor [owa] to the css styles in question.
So if you add

<style> [owa] .OutlookHide { display: none } </style>

to your head, and add the OutlookHide class to the table that contains your form, it won't show in Outlook.com

I was looking for that conditional the last 4 weeks and couldn't find it. Even now that I know that [owa] conditional exist I can't find any documentation about it on the web, from where do you know this?

I honestly can't remember where I got it from, or I would have credited that source.

To clarify: It doesn't matter what you write in the attribute selector (as long as it's not too common). The trick is, that Outlook.com/Hotmail strips the Attribute Selector from mails, but leaves the rest of the css rule intact.
Other mail clients will either strip (gmail) or filter (yahoo) css rules with attribute selectors, or leave them entirely intact, so the selector will keep the css from being applied.

For other people reading this:
The client and we decided that it is too risky to send a form in a mail. The factor that people are not used to input anything in their mails weighs higher than if it is even possible or not.

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